We apply the recent results in Loop Quantum Cosmology and in the resolution of Black Hole singularity to the gravitational collapse of a star. We study the dynamic of the space time in the interior of the Schwarzschild radius. In particular in our simple model we obtain the evolution of the matter inside the star and of the gravity outside the region where the matter is present. The boundary co...

A particularly simple model belonging to a wide class of coupled maps which obey a local conservation law is studied. The phase structure of the system and the types of the phase transitions are determined. It is argued that the structure of the phase diagram is robust with respect to mild violations of the conservation law. Critical exponents possibly determining a new universality class are c...

We investigate the effects of pair creation on the internal geometry of a black hole, which forms during the gravitational collapse of a charged massless scalar field. Classically, strong central Schwarzschild-like singularity forms, and a null, weak, mass-inflation singularity arises along the Cauchy horizon, in such a collapse. We consider here the discharge, due to pair creation, below the e...

We investigate the effects of pair creation on the internal geometry of a black hole, which forms during the gravitational collapse of a charged massless scalar field. Classically, strong central Schwarzschild-like singularity and a null, weak, mass-inflation singularity arises along the Cauchy horizon, in such a collapse. We consider here the discharge, due to pair creation, below the event ho...

Quantum gravity is the theory that is expected to successfully describe systems that are under strong gravitational effects while at the same time being of an extreme quantum nature. When this principle is applied to the universe as a whole, we use what is commonly named “quantum cosmology”. So far we do not have a definite quantum theory of gravity or cosmology, but we have several promising a...

Relating sedimentary records to seismic data is a major challenge. By shifting focus to a scale-invariant sharpness characterization for the reflectors, we develop an attribute that can capture and categorize the main reflector features, without being sensitive to amplitudes. Sharpness is defined by a scale exponent, which expresses singularity order and determines the reflection signature/wave...

Gravitational perturbations which are present in any realistic stellar collapse to a black hole, die off in the exterior of the hole, but experience an infinite blueshift in the interior. This is believed to lead to a slowly contracting lightlike scalar curvature singularity, characterized by a divergence of the hole’s (quasi-local) mass function along the inner horizon. The region near the inn...

Let Γ be a finite subgroup of Sp(V ). In this article we count the number of symplectic resolutions admitted by the quotient singularity V/Γ. Our approach is to compare the universal Poisson deformation of the symplectic quotient singularity with the deformation given by the Calogero-Moser space. In this way, we give a simple formula for the number of Q-factorial terminalizations admitted by th...

this article addresses an efficient and novel method for singularity-free path planning and obstacle avoidance of parallel manipulator based on neural networks. a modified 4-5-6-7 interpolating polynomial is used to plan a trajectory for a spherical parallel manipulator. the polynomial function which is smooth and continuous in displacement, velocity, acceleration and jerk is used to find a pat...

We determine the derived representation type of Nakayama algebras and prove that a tame algebra without simple projective module is gentle or equivalent to some skewed-gentle algebra, as consequence, we its singularity category.